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70 SUPERSTAR II User Manual Rev 3
Appendix G GPS Overview
Figure 23: Accuracy versus Precision
1
G.3.1 Single-Point vs. Relative Positioning
In single-point positioning, coordinates of a GPS receiver at an unknown location are sought with respect to the
earth's reference frame by using the known positions of GPS satellites being tracked. The position solution
generated by the receiver is initially developed in earth-centered coordinates which can subsequently be
converted to any other coordinate system. With as few as four GPS satellites in view, the absolute position of
the receiver in three-dimensional space can be determined. Only one receiver is needed.
In relative positioning, also known as differential positioning, the coordinates of a GPS receiver at an unknown
point (the “rover” station) are sought with respect to a GPS receiver at a known point (the “base” station). The
concept is illustrated in Figure 24, Example of Differential Positioning on Page 71. The relative-position
accuracy of two receivers locked on the same satellites and not far removed from each other - up to tens of
kilometers - is extremely high. The largest error contributors in single-point positioning are those associated
with atmospheric-induced effects. These errors, however, are highly correlated for adjacent receivers and hence
cancel out in relative measurements. Since the position of the base station can be determined to a high degree of
accuracy using conventional surveying techniques, any differences between its known position and the position
computed using GPS techniques can be attributed to various components of error as well as the receiver’s clock
bias. Once the estimated clock bias is removed, the remaining error on each pseudorange can be determined.
The base station sends information about each satellite to the rover station, which in turn can determine its
position much more exactly than would be possible otherwise.
The advantage of relative positioning is that much greater precision (<1 m, depending on the method and
environment) can be achieved than by single-point positioning. In order for the observations of the base station
to be integrated with those of the rover station, relative positioning requires either a data link between the two
stations (if the positioning is to be achieved in real-time) or else post-processing of the data collected by the
rover station. At least four GPS satellites in view are still required. The absolute accuracy of the rover station’s
computed position will depend on the accuracy of the base station’s position.
1.Environment Canada, 1993, Guideline for the Application of GPS Positioning, p. 22.
© Minister of Supply and Services Canada
High accuracy,
high precision
High accuracy,
low precision
Low accuracy,
low precision
Low accuracy,
high precision